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Changing the order of triple summation

  1. Jul 9, 2012 #1
    1. The problem statement, all variables and given/known data
    I want to change the order of triple summation. it follows:
    $$\sum^N_{k=0} f(k) \sum^k_{n=0}\sum^{N-k}_{m=0} g(k,n)h(k,m)A(n+m)$$

    =>
    I need to set the variable x(=n+m) go from 0 to N firstly, and then further go on...
    $$\sum^N_{x=0} A(x) \cdots \cdots$$

    But, I don't know how.... plz answer this question.
    Thank you very much

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    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 9, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    welcome to pf!

    hi hjcho! welcome to pf! :smile:
    let's write it in ordinary english …

    k can be anything (up to N), but n must be less than k, and m+k can be anything (up to N)

    ok, so how would we write it if we started with m? :wink:

    (hmm … are you sure that last N, above the ∑, shouldn't be an n ? :redface:)
     
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